Final Project for 1675
Exploring the Data
David Spellman
library(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.4 v dplyr 1.0.7
## v tidyr 1.1.3 v stringr 1.4.0
## v readr 2.0.1 v forcats 0.5.1## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()df <- readr::read_csv("cs_1675_fall2021_finalproject.csv", col_names = TRUE)## Rows: 1252 Columns: 11## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (1): m
## dbl (10): x1, x2, x3, x4, v1, v2, v3, v4, v5, output##
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.Take an initial look at the data and some basic statistics
df %>% glimpse ()## Rows: 1,252
## Columns: 11
## $ x1 <dbl> 0.025878, 0.030768, 0.019325, 0.306212, 0.031296, 0.031073, 0.0~
## $ x2 <dbl> 0.255934, 0.261575, 0.020877, 0.033379, 0.259342, 0.027119, 0.0~
## $ x3 <dbl> 0.492830, 0.498460, 0.258360, 0.255385, 0.264387, 0.260915, 0.0~
## $ x4 <dbl> 0.012770, 0.055779, 0.012424, 0.056190, 0.056594, 0.055192, 0.0~
## $ v1 <dbl> 0.275651, 0.343204, 4.998508, 5.090153, 5.031107, 9.977407, 0.2~
## $ v2 <dbl> 0.033657, 0.027082, 0.030259, 0.052342, 0.517705, 0.532436, 1.0~
## $ v3 <dbl> 1.166214, 1.260579, 1.298285, 1.322005, 1.368195, 1.298797, 1.1~
## $ v4 <dbl> 0.408402, 0.664248, 0.412870, 0.652111, 0.533701, 0.857509, 0.6~
## $ v5 <dbl> 0.525226, 2.866343, 0.409007, 0.861594, 6.451933, 0.958574, 0.2~
## $ m <chr> "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A"~
## $ output <dbl> 0.786, 0.730, 0.996, 0.326, 0.735, 0.954, 0.969, 0.986, 0.874, ~df %>% summary ()## x1 x2 x3 x4
## Min. :0.003117 Min. :0.001173 Min. :0.003344 Min. :0.001447
## 1st Qu.:0.144825 1st Qu.:0.059488 1st Qu.:0.180333 1st Qu.:0.034732
## Median :0.278602 Median :0.170552 Median :0.263551 Median :0.055822
## Mean :0.265192 Mean :0.159282 Mean :0.262674 Mean :0.053189
## 3rd Qu.:0.352812 3rd Qu.:0.238338 3rd Qu.:0.343556 3rd Qu.:0.072108
## Max. :0.609092 Max. :0.446306 Max. :0.509710 Max. :0.101868
## v1 v2 v3 v4
## Min. : 0.003474 Min. :0.002281 Min. : 1.003 Min. :0.01867
## 1st Qu.: 3.335833 1st Qu.:0.334104 1st Qu.: 3.945 1st Qu.:0.30184
## Median : 5.137150 Median :0.515154 Median : 5.632 Median :0.48923
## Mean : 5.079560 Mean :0.503186 Mean : 5.569 Mean :0.49132
## 3rd Qu.: 6.850576 3rd Qu.:0.684780 3rd Qu.: 7.189 3rd Qu.:0.67959
## Max. :10.133807 Max. :1.018897 Max. :10.177 Max. :0.97913
## v5 m output
## Min. : 0.006831 Length:1252 Min. :0.0070
## 1st Qu.: 2.439787 Class :character 1st Qu.:0.2517
## Median : 6.496589 Mode :character Median :0.4835
## Mean : 5.867330 Mean :0.5311
## 3rd Qu.: 9.328919 3rd Qu.:0.8430
## Max. : 9.999845 Max. :0.9990ddf <- df %>% select(-m)
stats <- tibble::tibble (variable = names (ddf),
num_missing = map_dbl (ddf, ~ sum (is.na (.))),
num_unique = map_dbl (ddf, n_distinct),
min_value = map_dbl (ddf, min),
median_value = map_dbl (ddf, median),
max_value = map_dbl (ddf, max))
stats %>% knitr::kable (caption = "variables overview")| variable | num_missing | num_unique | min_value | median_value | max_value |
|---|---|---|---|---|---|
| x1 | 0 | 1245 | 0.003117 | 0.2786015 | 0.609092 |
| x2 | 0 | 1250 | 0.001173 | 0.1705525 | 0.446306 |
| x3 | 0 | 1250 | 0.003344 | 0.2635515 | 0.509710 |
| x4 | 0 | 1235 | 0.001447 | 0.0558215 | 0.101868 |
| v1 | 0 | 1252 | 0.003474 | 5.1371505 | 10.133807 |
| v2 | 0 | 1249 | 0.002281 | 0.5151535 | 1.018897 |
| v3 | 0 | 1252 | 1.002923 | 5.6319045 | 10.176830 |
| v4 | 0 | 1252 | 0.018665 | 0.4892350 | 0.979126 |
| v5 | 0 | 1252 | 0.006831 | 6.4965890 | 9.999845 |
| output | 0 | 690 | 0.007000 | 0.4835000 | 0.999000 |
df %>% select (- output) %>% distinct () %>% dim ()## [1] 1252 10First we will graph the response in respect to each of the x inputs.
df %>% ggplot (mapping = aes (x = x1, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Based on this graph it looks like the response becomes worse as x1 becomes greater
The best x1 values based on this graph seem to fall between 0.1 to 0.3
df %>% ggplot (mapping = aes (x = x2, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x3, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x4, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now for calculating and plotting the x5 calculated input, as well as calculating w, t, and z for other plots.
### calculate x5, z, w, and t.
dfT <- (df %>% tibble::as_tibble () %>% mutate (x5 = (1 - (x1 + x2 + x3 + x4)), w = (x2 / (x3 + x4)), z = ((x1 + x2) / (x4 + x5)), t = (v1 * v2)))
### plot output against x5
dfT %>% ggplot (mapping = aes (x = x5, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated w input.
dfT %>% ggplot (mapping = aes (x = w, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated z input.
dfT %>% ggplot (mapping = aes (x = z, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now we will graph the response in respect to each of the v inputs.
df %>% ggplot (mapping = aes (x = v1, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v2, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v3, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v4, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v5, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Plotting the output in terms of the calculated t input.
dfT %>% ggplot (mapping = aes (x = t, y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Try the same graphs above but now binned by machine used to produce mixture.
First we will graph the response in respect to each of the x inputs as before.
df %>% ggplot (mapping = aes (x = x1, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x2, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x3, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x4, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Now for visualizing the inputs derived by the x inputs binned by machine.
dfT %>% ggplot (mapping = aes (x = x5, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated w input binned by machine.
dfT %>% ggplot (mapping = aes (x = w, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated z input binned by machine.
dfT %>% ggplot (mapping = aes (x = z, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Now we will graph the response in respect to each of the v inputs.
df %>% ggplot (mapping = aes (x = v1, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v2, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v3, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v4, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v5, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Plotting the output in terms of the calculated t input binned by machine.
dfT %>% ggplot (mapping = aes (x = t, y = output)) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Try plotting with logit transformation applied to the response.
df %>% ggplot (mapping = aes (x = x1, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x2, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x3, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x4, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now for calculating and plotting the x5 calculated input, as well as calculating w, t, and z for other plots.
### calculate x5, z, w, and t.
dfT <- (df %>% tibble::as_tibble () %>% mutate (x5 = (1 - (x1 + x2 + x3 + x4)), w = (x2 / (x3 + x4)), z = ((x1 + x2) / (x4 + x5)), t = (v1 * v2)))
### plot output against x5
dfT %>% ggplot (mapping = aes (x = x5, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated w input.
dfT %>% ggplot (mapping = aes (x = w, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated z input.
dfT %>% ggplot (mapping = aes (x = z, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now we will graph the response in respect to each of the v inputs.
df %>% ggplot (mapping = aes (x = v1, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v2, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v3, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v4, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v5, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Plotting the output in terms of the calculated t input.
dfT %>% ggplot (mapping = aes (x = t, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now visualized the logistic response binned by machine as well.
df %>% ggplot (mapping = aes (x = x1, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x2, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x3, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = x4, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Now for visualizing the inputs derived by the x inputs binned by machine.
dfT %>% ggplot (mapping = aes (x = x5, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated w input binned by machine.
dfT %>% ggplot (mapping = aes (x = w, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Visualizing calculated z input binned by machine.
dfT %>% ggplot (mapping = aes (x = z, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Now we will graph the response in respect to each of the v inputs.
df %>% ggplot (mapping = aes (x = v1, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v2, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v3, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v4, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
df %>% ggplot (mapping = aes (x = v5, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Plotting the output in terms of the calculated t input binned by machine.
dfT %>% ggplot (mapping = aes (x = t, y = boot::logit (output))) + geom_point () + geom_smooth (method = lm) + facet_wrap (~m)## `geom_smooth()` using formula 'y ~ x'
Let’s start with plotting wx1 against the output to see if they are correlated.
dfT %>% ggplot (mapping = aes (x = (w * x1), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now let’s do the same check for x5w.
dfT %>% ggplot (mapping = aes (x = (x5 * w), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now let’s do the same check for the values used to calculate w: x2, x3, and x4.
dfT %>% ggplot (mapping = aes (x = (x2 * w), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x3 * w), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x4 * w), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now check z for the same correlations.
dfT %>% ggplot (mapping = aes (x = (x1 * z), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x2 * z), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x3 * z), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x4 * z), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x5 * z), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now check x5 against the other four x inputs.
dfT %>% ggplot (mapping = aes (x = (x1 * x5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x2 * x5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x3 * x5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x4 * x5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now let’s check the interactions between the plain x inputs.
dfT %>% ggplot (mapping = aes (x = (x2 * x1), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x3 * x1), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x4 * x1), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now with x2 instead of x1.
dfT %>% ggplot (mapping = aes (x = (x3 * x2), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (x4 * x2), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now x3 in the interaction instead of x2.
dfT %>% ggplot (mapping = aes (x = (x4 * x3), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now to look for correlations among the v inputs.
Check for correlations between the derived t input and the five v inputs.
dfT %>% ggplot (mapping = aes (x = (v1 * t), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v2 * t), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v3 * t), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v4 * t), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v5 * t), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now check v5 against the other four v inputs.
dfT %>% ggplot (mapping = aes (x = (v1 * v5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v2 * v5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v3 * v5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v4 * v5), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now let’s check the interactions between the plain v inputs.
dfT %>% ggplot (mapping = aes (x = (v2 * v1), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v3 * v1), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v4 * v1), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now with v2 instead of v1.
dfT %>% ggplot (mapping = aes (x = (v3 * v2), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
dfT %>% ggplot (mapping = aes (x = (v4 * v2), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'
Now v3 in the interaction instead of v2.
dfT %>% ggplot (mapping = aes (x = (v4 * v3), y = output)) + geom_point () + geom_smooth (method = lm)## `geom_smooth()` using formula 'y ~ x'